June 2nd, 2010, 12:52 pm
The paper stars by considering a forward rate agreement. The formula presented is for the FRA at time 0 is: KL is the fixed rate between dates t0 and t1 and fixing in theta. The rate L(theta) is the LIBOR rate fixing in theta for the period t0-t1. The accrual factor between t0 and t1 is delta and discounted from maturity t1 and t0 at the fixing rate L(theta). The payoff in t0 isThe curve to be used in the contingent claim pricing is the funding curve. The discount factors or zero-coupon prices viewed from t to maturity u are denoted P(t,u). The price is the payoff fixed in theta paid in t0 and invested at the cost of funding to t1. The payment in t1 is chosen like the standard approach to FRA or caplet pricing. The P(.,t1) numerarire will be used to simplify the computation. In that numerarire the funding rate F associated to L is a martingale. I dont really understand this formula and dont see how the different times converges to 0. The N0 and Nt1 numerarires is the discount factor from 0 to t1 so the payment i am discounting must be in t1. the payment of the FRA after discounting at the LIBOR fixing in theta leaves the cashflow at t0 (or the fixing date). So this payment has to be placed in t1 si the N0/Nt1 makes sense. But the payment is multiplied by P(theta,t1) which is actually a discount. If the term used instead were P(theta,t1)^-1 that would make sense but i dont see how that formula is correct................Thanks....